You could also use actionscript to do snow, its easier than animating it.
This tutorial pretty easy to understand and has a .fla that you can use.
Btw change the width and height to Stage.width and Stage.height, so it automatically changes to your stage's width and height
init = function () {
width = Stage.width;
// pixels
height = Stage.height;
// pixels
and remove the t.wind line (line 17) if you want it to fall without the random movement